In the context of vector field data visualization, it is often desirable to construct a hierarchical data representation. One
possibility to construct a hierarchy is based on clustering
vectors using certain similarity criteria. We combine two
fundamental approaches to cluster vectors and construct
hierarchical vector field representations. For clustering, a
locally constructed linear least-squares approximation is
incorporated into a similarity measure that considers both
Euclidean distance between point pairs (for which dependent vector
data are given) and difference in vector values. A modified
normalized cut (NC) method is used to obtain a near-optimal
clustering of a given discrete vector field data set. To obtain a
hierarchical representation, the NC method is applied recursively
after the construction of coarse-level clusters. We have applied
our NC-based segmentation method to simple, analytically defined
vector fields as well as discrete vector field data generated by
turbulent flow simulation. Our test results indicate that our
proposed adaptation of the original NC method is a promising
method as it leads to segmentation results that capture the
qualitative and topological nature of vector field data.
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